Methods of improving quantum LADARs and related sensors are developed based on quantum entanglement and hyperentanglement. Multiple single photon states are used to obtain a multiphoton entangled state. These states can be N00N states, M&N states (M&N), or a linear combination of M&N states (LCMNS) or generalized states kindred to LCMNS. The procedure for doing this derives from the fundamental theorem of algebra. Various states generated by this process are developed. A diagram of a device for producing such states is examined. They are related to a simpler version of this concept introduced in the seminal experiment by Mitchell-Lundeen and Steinberg. A certain class of states obtained through the Schrodinger kitten process are shown to be effective for generating states hyper-entangled in polarization and energy-time. A diagram of a device for producing such states is considered. Alternate methods of generating hyperentanglement in polarization and energy-time are discussed. Improvements offered by networks are discussed. The utility of these procedures for sensing and communications is examined. An open systems analysis based on density operator theory is conducted including both noise and loss mechanisms. The susceptibility to noise and loss of the various hyper-entanglement procedures is examined. Various measures of effectiveness (MOEs) are derived to quantize system performance. MOEs include but are not limited to, SNR, signal-to-interference ratio, quantum Cramer Rao’ lower bound, quantum Chernoff bound, measurement time, the Holevo bound, sensing range, and resolution. A summary table with expanded MOEs results drawing from multiple papers is provided.
Methods of improving quantum LADARs and related sensors are developed based on quantum entanglement and hyperentanglement. Multiple single photon states are used to obtain a multiphoton entangled state. These states can be N00N states, M&N states (M&N), or a linear combination of M&N states (LCMNS) or generalized states kindred to LCMNS. The procedure for doing this derives from the fundamental theorem of algebra. Various states generated by this process are developed. A diagram of a device for producing such states is examined. They are related to a simpler version of this concept introduced in the seminal experiment by Mitchell-Lundeen and Steinberg. A certain class of states obtained through the Schrodinger kitten process are shown to be effective for generating states hyper-entangled in polarization and energy-time. A diagram of a device for producing such states is considered. Alternate methods of generating hyperentanglement in polarization and energy-time are discussed. Improvements offered by networks are discussed. The utility of these procedures for sensing and communications is examined. An open systems analysis based on density operator theory is conducted including both noise and loss mechanisms. The susceptibility to noise and loss of the various hyper-entanglement procedures is examined. Various measures of effectiveness (MOEs) are derived to quantize system performance. MOEs include but are not limited to, SNR, signal-to-interference ratio, quantum Cramer Rao’ lower bound, quantum Chernoff bound, measurement time, the Holevo bound, sensing range, and resolution. A summary table with expanded MOEs results drawing from multiple papers is provided.
Quantum hyper-entanglement, multi-photon entanglement and quantum networks are combined to develop enhanced sensing capabilities. Quantum hyper-entanglement refers to entanglement in more than one degree of freedom, e.g. polarization, energy-time, orbital angular momentum (OAM), and frequency. Multi-photon entanglement involves entanglement typically between more than two photons, whereas hyper-entanglement is generally described as occurring between two photons referred to as the signal and ancilla photon. Multi-photon states representing an increasing hierarchy of robustness are discussed. These include N00N states, M&N states and linear combinations of M&N states. A M&N state, the (N, 1) states is shown to be very useful. A method of constructing M&N states using Shrodinger kitten states is considered. Multi-photon entanglement and hyper-entanglement are combined for enhanced sensing. This combined approach permits improvement in measures of effectiveness (MOEs) like SNR, signal to interference ratio (SIR), time-on-target (TOT), Holevo bound, and system range. The combined approach yields significant improvements in resolution both by permitting an effective reduction in wavelength used for measurement as well as decreasing the related Cramer Rao lower bound. This in turn permits sensors based on these concepts to have enhanced parameter estimation capabilities. These parameters can include range, bearing and elevation. Additional enhancements are found by combining the multi-photon hyper-entangled states with the idea of a quantum network. Quantum networks are a collection of nodes that may have quantum memory. This approach can significantly reduce loss; offer noise and interference resistance; decrease measurement error; and reduce size, weight, power and costs (SWAPC) for the overall system.
Quantum systems combining various forms of quantum entanglement, quantum networks and wavefront design via Lie optics are discussed. The forms of entanglement include multiphoton entanglement and hyperentanglement, with an emphasis on hybrid states born of combining these two forms of entanglement. Lie optics refers to the use of Lie algebra techniques in optics. Improvements born of combining these techniques are discussed in terms of various measures of effectiveness (MOE) including: signal-to-noise ratio (SNR); signal-to-interference ratio (SIR); quantum Cramer Rao lower bound (QCRLB); classical Cramer Rao lower bound (CCRLB); measurement time (MT); quantum Chernoff bound; sensing range; communications range; phase and angular resolution; size, weight, power and costs (SWAPC); various measures associated with information content of signals; superdense coding; and the Holevo bound. Quantum networks coupled with hyperentanglement increase the likelihood that samples are statistically independent improving both classical and quantum estimation results. This can reduce both estimation uncertainty and measurement time. Quantum networks also offer opportunities for additional processing of signals exploiting signal processing, information fusion, adaptive optics and other techniques. Wavefronts designed using Lie optics offer additional advantages in terms of reduced diffraction, the ability to design self-accelerating curves to enhance sensing and communications, and improved MOE values in all categories. The utility of three different types of designed wavefronts in terms of MOEs are discussed. Combining hybrid states with wavefronts designed using Lie optics offers significant MOE improvements greatly expanding communication range, sensing range and significantly improving the information carrying content of signals. Extensive numerical results are provided.
Novel multiphoton entangled states have been developed, which offer utility for sensors. These states are linear combinations of M&N states (LCMNS). Closed form expressions for the coefficients have been derived that result in states offering sensitivities far greater than those found in the literature. Adaptive optics procedures have been conceived that permit these coefficients to be determined. LCMNS can also be used to generate high quality hyperentangled states. Various states generated by this process are developed. The utility of these procedures for quantum interferometry and RF signal detection is examined. The susceptibility to loss of the various interferometry and RF detection approaches is examined using an open systems analysis. The novel quantum interferometer uses adaptive optics, which offers a huge improvement in phase sensitivity over previous interferometers, while greatly reducing the number of photons used. Large numbers of photons can contribute to vibration reducing sensitivity. The approach based on entanglement presented here, even in the presence of loss can reduce the number of photons used significantly, while enhancing phase sensitivity. The new interferometer simultaneously minimizes phase error, maximizes visibility and greatly reduces the number of photons used. When the interferometer employing LCMNS is combined with an atomic RF antenna, E-field sensitivity is increased to a value nearly 400,000 times that found in the literature. Extensive numerical results are provided comparing phase sensitivity, visibility and E-field sensitivity for LCMNS, N00N states, and non-entangled states. LCMNS offer huge improvements in sensitivity compared to other approaches.
Methods of generating N00N, M&N, linear combinations of M&N states as well as more complicated quantum entangled and quantum hyper-entangled states will be considered. Quantum hyper-entanglement refers to quantum entanglement in more than one degree of freedom, e.g. energy-time, polarization, orbital angular momentum, etc. Internal noise and loss within the entanglement or hyper-entanglement generators and external noise and loss due to atmospheric effects and detectors are modeled. Analysis related to the devices that generate these entangled or hyperentangled states will be provided. The following will be derived: closed form expressions for wave function normalization, wave function, density operator, reduced density operator, phase error bound, the symmetrized logarithmic derivative, the quantum Fisher information, the quantum Cramer-Rao lower bound, the relevant projection operators and the related probability of detection expressions. Generation and detection of the entangled or hyperentangled states will be considered. The entanglement generators will use linear and nonlinear optical devices. Optimization criteria for the quantum states, generation and detection schemes and designs optimal with respect to the criteria will be discussed. Applications of the generated states for producing super sensitivity and super resolution will be discussed. The fundamental role of coincidence measurement for generating entanglement is included. Hyperentanglement offers N times classical resolution, where N is a quantum number associated with the system.
A network based on quantum information has been developed to improve sensing and communications capabilities. Quantum teleportation offers features for communicating information not found in classical procedures. It is fundamental to the quantum network approach. A version of quantum teleportation based on hyper-entanglement is used to bring about these improvements. Recently invented methods of improving sensing and communication via quantum information based on hyper-entanglement are discussed. These techniques offer huge improvements in the SNR, signal to interference ratio, and time-on-target of various sensors including RADAR and LADAR. Hyper-entanglement refers to quantum entanglement in more than one degree of freedom, e.g. polarization, energy-time, orbital angular momentum (OAM), etc. The quantum network makes use of quantum memory located in each node of the network, thus the network forms a quantum repeater. The quantum repeater facilitates the use of quantum teleportation, and superdense coding. Superdense coding refers to the ability to incorporate more than one classical bit into each transmitted qubit. The network of sensors and/or communication devices has an enhanced resistance to interference sources. The repeater has the potential for greatly reducing loss in communications and sensor systems related to the effect of the atmosphere on fragile quantum states. Measures of effectiveness (MOEs) are discussed that show the utility of the network for improving sensing and communications in the presence of loss and noise. The quantum repeater will reduce overall size, weight, power and cost (SWAPC) of fielded components of systems.
New results have been derived for wavefronts for single and multiple photons and combined with quantum hyperentanglement, multiphoton entanglement, and network properties. These new results arise from use of Lie algebra techniques for disentanglement of certain operators related to propagation. The new results include closed form exact expressions for functions related to the disentanglement process. These expressions permit many different solutions to the disentanglement process. These new expressions offer much higher order programmable self-accelerating curves to be created. This in turn facilitates more effective quantum-based sensing and communication around corners and other obstacles, with reduced loss. This approach significantly increases the information that can be communicated or stored when using a recently derived extension of superdense coding. The resulting wavefronts are shown to reduce diffraction and have the self-healing property, i.e. automatically reobtain their original form when initially damaged by turbulence. Each node of the network will transmit at least one signal and one ancilla photon in a hyper-entangled state. Parameters used for hyper-entanglement will include photon polarization, energy-time, orbital angular momentum, radial quantum number, etc. as well as up to 12 parameters characterizing the wavefront properties. Eigenfunctions of operators associated with each 2D paraxial wave equation will be determined each being a function of up to six parameters. The same wavefront or combinations of wavefronts can be applied to multiple photons to combine hyper-entanglement with multiphoton entanglement offering additional improvements. Measures of effectiveness such as the signal-to-noise ratio (SNR), measurement time, resolution measures, and Holevo bound are considered.